The chance to reclaim the state’s highest office next year has Republicans tripping over each other — but finding a would-be challenger to go up against Democrat Chris Murphy belongs on the back of a milk carton.

So far, no one in the GOP is committing to what national handicappers term a yeoman’s task — and an expensive one. It’s led them to categorize the seat of Murphy, who is finishing up his first six-year term and making noise nationally on progressive causes, as safe.

“I think whoever comes out is going to have to spend more than that because nobody is going to know who they are,” said Jennifer Duffy, senior editor of the nonpartisan Cook Political Report in Washington, D.C. “I don’t think a relative unknown could do it for less than $25 million.”

State GOP Chairman J.R. Romano said at least four Republicans have signaled their interest in the race, three of whom he has spoken with about the prospect. He declined to identify them, but said some are sitting office holders.

“Listen, there’s no question that money is a major factor when it comes to these races,” Romano said. “Republicans have to start believing that we can win these races and we can when you look inside the numbers. No candidate, no person is a shoe-in to win election. I think the presidential election taught us that.”

Among the names who have put out feelers on the race, Hearst Connecticut Media has learned, is state Sen. Tony Hwang, R-Fairfield. A request for comment was left Tuesday for Hwang, who is in his second term in the Senate after three terms in the House.

Hwang’s ambitions for higher office are hardly a secret, with the ever-present lawmaker setting up an exploratory committee for unspecific statewide office in 2015. That vessel had $1,600 in the bank as of January, according to filings with the state Elections Enforcement Commission.

In contrast, Murphy last week touted raising $2 million from 55,000 contributors since the beginning of the year, with the average donation being $40. That’s a mere pittance of the $10.5 million that Murphy spent in 2012 and the $50 million onslaught of his GOP opponent, Linda McMahon. Now the head of Donald Trump’s Small Business Administration, McMahon shelled out $50 million on her 2010 Senate run against Blumenthal, who spent $8.7 million.

“As you know, Connecticut can be pretty expensive if you do a lot of TV in the New York market,” Duffy said.

The last time Republicans won a statewide or congressional race in Connecticut was 2006, but the GOP minority has been champing at the bit over its gubernatorial prospects for next year. Incumbent Democrat Dannel P. Malloy, whose job approval ratings have been ham-strung by budget deficits and the loss of General Electric’s headquarters to Boston, is undecided on whether he will seek a third term.

“The problem for Republicans is you don’t have a deep bench,” said Duffy, who has classified the governor’s race as “leans Democrat.” “Republicans seem a little more focused on Malloy than they do on the Senate race. Whoever does run isn’t going to be able to count on a lot of help from national Republicans because there are lots of more winnable races ahead of Connecticut.”

There are 34 Senate seats up for grabs in 2018, 10 of which are held by Democrats who come from states carried by Trump.